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Networks are commonly used to model the traffic patterns, social interactions, or web pages. The nodes in a network do not possess the same characteristics: some nodes are naturally more connected and some nodes can be more important. Closeness centrality~(CC) is a global metric that quantifies how important is a given node in the network. When the network is dynamic and keeps changing, the relative importance of the nodes also changes. The best known algorithm to compute the CC scores is not practical to recompute them from scratch after each modification. In this paper, we propose Streamer, a distributed memory framework for incrementally maintaining the closeness centrality scores of a network upon changes. It leverages pipeline parallelism, takes the NUMA effects into account, and proves to be scalable. The design we propose makes the CC maintenance within dynamic networks feasible in real time.